ON THE EQUIVALENCE OF SPATIAL AND TEMPORAL STABILITY FOR TRANSLATION INVARIANT LINEAR RESISTIVE-NETWORKS

This paper explores a fundamental relationship between spatial and temporal stability for a class of translation-invariant linear resistive networks. These networks appear to have great promise for the high-speed linear filtering of two-dimensional spatially sampled analog data such as imagery. In general, networks designed for such applications require both positive and negative resistances. We prove that such networks-when terminated in a certain reasonable manner-are temporally asymptotically stable in the presence of arbitrary parasitic capacitances whenever the network's underlying spatial response (convolution) is bounded-input bounded-output stable.